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For shelves, maybe the packing density of randomly oriented cuboids isn't any better than cans.

(There's a practical use of math for you.)

Random orientation is the key, "pretty good kinda aligned face out" is very fast and cheap both WRT labor and capital, and label alignment on the can is not a cost at all.

On cuboids the label alignment is beyond critical (even just randomly off center 1/4 inch on the shelf would look awful) and the capital cost to align the cubioids perfectly in their box and on the shelf are expensive.

(edited to add, I'm not saying our economic system would collapse if the cost of cuboid soup cans went up three cents a piece, but it would be an incredibly difficult corporate sell to convince one mfgr of many that he should accept a 1/3 of a million dollar loss compared to his round competitors on ten million units sold just to make them cube-ish, for, uh, fun)

Also wear in the box. Cuboids would tend to wear off entire faces of the label while being tossed around the warehouse but cylinders at worst will end up with a vertical streak.

Finally having worked retail as a starving student a quarter century ago there is a huge installed base of semi-standardized grocery store shelving that was never designed for the peculiar spacing cubiods would require. Or rephrased, cylindrical cans and rectangular prism boxes have evolved over decades to fit certain semi-standard discrete shelf configurations... If you want it on an American supermarket shelf, then a grid pattern of X by Y (preferably one shipping crate) will take up a certain discrete space. Not a quarter inch too big necessitating reconfiguration of the whole section, etc.

Who says they'd be randomly oriented? When I see examples of cuboid products on shelves (think boxes), they're usually stacked quite neatly and efficiently.

That's because some poor sap has to organize them every night. (Source: was once that poor sap)

Nothing exhibits the Second Law of Thermodynamics quite like grocery store shelves.

Not quite what you ask for, but it may interest some: http://en.m.wikipedia.org/wiki/Percolation_threshold#Thresho...

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